Electron helical orbits in microwave free electron lasers (FELs) using helical wigglers and an axial guide field become unstable as beam current saturation is reached. Because the instability does not appear before saturation occurs, P. Volbeyn et al., "Measurement of the temporal and spatial phase variations of a pulsed free electron laser amplifier," 22 IEEE Trans. Plasma Sci., pg. 659 (1994), surmise that the instability is driven by the radio frequency electromagnetic fields (rf) and not the beam's own space charge fields. The particle loss resulting from the instability appears to effect the overall extraction efficiency of helical-wiggler FELs.
An annular electron beam was considered by B. E. Carlsten, "Stable off-axis electron orbits in a logitudinal-wiggler free-electron laser," 78 J. Appl. Phys., No. 4, pp. 2811-2816, (1995), for use with kiloampere microwave FELs in order to increase the power output of these devices. An annular electron beam means an electron beam that is annularly disposed about the axis of the direction of travel of the electrons and the electrons travel in a cylindrical pattern in close proximity to the surrounding cavity structure with each electron traversing a helical orbital path along the direction of travel. Orbit stability issues become especially important for this type of electron beam because of the typical small beam-to-wall spacing.
Most microwave FEL experiments have used mildly relativistic (500 keV-1 MeV) pencil axial electron beams interacting with TE.sub.11 (transverse electric) modes. Since only the electric field can modify the total energy of an electron, it is clear that the power extracted from the electron beam, if any, comes from the coupling of the transverse electron motion with the transverse electric field of the rf for this type of FEL. However, the transverse magnetic field can modify the total transverse force on a particle.
The net transverse force on an electron is given by EQU F.sub.x =e(E.sub.x -v.sub.z B.sub.y)=eE.sub.x (1-.beta..sub.z),Eqn. (1)
where E.sub.x is the transverse electric field, B.sub.y is the transverse magnetic field, v.sub.z is the axial electron velocity, and .beta..sub.z is the axial velocity normalized to the speed of light. For relativistic beams the net transverse force scales as 1-.beta..sub.z .apprxeq..gamma..sup.-2 /2, where .gamma. is the relativistic mass factor, which quickly becomes small as the beam energy is increased. Although the coupling between the motion of an electron and the rf is through the transverse electron motion, the power is efficiently extracted from the axial electron motion. This is one reason why the FEL scales nicely for high power operation with relativistic beams (&gt;10 MeV) at optical wavelengths. Note that the net axial force is given by EQU F.sub.z =eE.sub.x .beta..sub.x, Eqn. (2)
which is much smaller than the transverse force induced by either the rf magnetic or electric field.
From symmetry considerations a TE.sub.0m rf mode has been proposed to interact with an annular electron beam with helical orbits. However, helical wiggler FELs operating with microwave TE modes have much larger transverse forces than those for optical FELs at high energy and these forces lead to inherently unstable electron orbits that, in turn, result in phase and energy incoherence as power is extracted from the electrons.
Accordingly, it is an object of the present invention to provide an FEL with relatively stable electron orbits in an annular beam even with large extraction efficiencies.
It is another object of the present invention to provide an FEL where the rf axial electric field interacts with the electron beam
Additional objects, advantages and novel features of the invention will be set forth in part in the description which follows, and in part will become apparent to those skilled in the art upon examination of the following or may be learned by practice of the invention. The objects and advantages of the invention may be realized and attained by means of the instrumentalities and combinations particularly pointed out in the appended claims.